Product sorting drop-down menu hiding ?

Hi,
I would like to hide the Sorting drop-down menu and “show xxx product per page” drop-down menu (above products),
I found this code:

div .product-sorting {
display: none;
}

That work, but I would like to hide the sorting drop-down menu only in my home page
(I use a Avia Product grid to display some products in my home page)
but I want to keep it in the woocommerce product page.

Second question:
Is it possible to display the sorting drop-down menu (sort by date, by price, by name…) but hide the other drop-down menu “show xxx product per page” ?

Third question:
Is it possible to move the sorting drop-down menu (sort by date, by price, by name…and show xxx product per page) in a sidebar ?
I dont find any widget to make this, but it is surely possible ?
Regards,

Alain